Preheat a large cast-iron skillet over medium-high.
In another large skillet, heat the oil over medium-high. Add the bacon and cook, stirring, until crispy, about 3 minutes. Transfer bacon to paper towels. Pour off excess fat from skillet and add 2 tbsp. butter. When butter stops foaming, add the shallots, celery, thyme, chile and garlic; season with salt and pepper. Cook, stirring often, until the vegetables soften, 2 to 3 minutes. Stir in the sherry, scraping up any browned bits. Add the crab, lemon juice, Old Bay and mustard. Season with Tabasco to taste and cook 2 minutes. Cover and remove from the heat.
Season the beef. Add 2 tbsp. butter to the cast-iron skillet; when it stops foaming, add the beef and cook until browned, about 4 minutes per side for medium-rare. Transfer to a warm plate.
To the same skillet, add the remaining 2 tbsp. butter; when it foams, add the radishes and season. Cook, stirring occasionally, until crisp-tender, 3 to 4 minutes. Stir in the chives.
Place the toast on plates; top with the beef and the crab mixture. Garnish with the bacon and parsley. Serve with the radishes.